Risk, Return, and Historical Record (Essentials of Investments 12th Ed) PDF

Chapter Risk, Return and the 5 Historical Record Bodie, Kane, and Marcus Essentials of Investments 12th Edition  5.1 Rates of Return Holding-Period Return (HPR) Rate of return over given investment period...

Chapter Risk, Return and the 5 Historical Record Bodie, Kane, and Marcus Essentials of Investments 12th Edition  5.1 Rates of Return Holding-Period Return (HPR) Rate of return over given investment period PEnding − PBeginning + DivCash HPR = PBeginning Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 2  5.1 Rates of Return: Example What is the HPR for a share of stock that was purchase for $25, sold for $27 and distributed $1.25 in dividends? $27.00– $25.00 + $1.25 𝐻𝑃𝑅 = = 0.13 = 13.00% $25.00 The HPR is the sum of the dividend yield plus the capital gains yield Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 3  5.1 Rates of Return: Measuring over Multiple Periods Arithmetic average Sum of returns in each period divided by number of periods Geometric average Single per-period return Gives same cumulative performance as sequence of actual returns Dollar-weighted average return Internal rate of return on investment Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 4  5.1 Rates of Return: Measuring over Multiple Periods Arithmetic average: The sum of the returns divided by the number of years. r1 + r2 +... + rn rArithmetic = n 10 + 25 − 20 + 20 = =.0875 = 8.75% 4 Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 5  5.1 Rates of Return: Measuring over Multiple Periods Geometric average: Single period return that gives the same cumulative performance as the sequence of actual returns rGeometric = [(1 + r1 )  (1 + r2 ) ...  (1 + rn )]1/ n − 1 = 1.10 1.25 .80 1.20 − 1 = 0.0719 = 7.19% 1/4 Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 6  5.1 Rates of Return Dollar-weighted average return The internal rate of return on an investment Annualizing Rates of Return APR = Annual Percentage Rate Per-period rate × Periods per year Ignores Compounding EAR = Effective Annual Rate Actual rate an investment grows Does not ignore compounding Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 7  5.1 Rates of Return: EAR vs. APR n-Periods of Compounding: Continuous Compounding:  APR  n EAR = e APR − 1 EAR = 1 +  −1  n  APR = [( EAR + 1)1/ n − 1]  n APR = ln( EAR + 1) where n = compounding per period Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 8 5.2 Inflation and The Real Rates of Interest Nominal Interest and Real Interest 1 + rNom 1 + rReal = 1+ i where rReal = Real Interest Rate rNom = Nominal Interest Rate i = Inflation Rate Example: What is the real return on an investment that earns a nominal 10% return during a period of 5% inflation? 1 +.10 1 + rReal = = 1.048 1 +.05 r =.048 or 4.8% Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 9 5.2 Inflation and The Real Rate of Interest Equilibrium Nominal Rate of Interest Fisher Equation (5.9) rNom = rReal + E (i ) Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 10 Figure 5.1 Inflation and Interest rates (1927-2018) Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 11  5.3 Risk and Risk Premiums Scenario Analysis and Probability Distributions Scenario analysis: Possible economic scenarios; specify likelihood and HPR Probability distribution: Possible outcomes with probabilities Expected return: Mean value Variance: Expected value of squared deviation from mean Standard deviation: Square root of variance Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 12  Spreadsheet 5.1 Scenario Analysis for a Stock Index Fund Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 13  5.3 Risk and Risk Premiums The Normal Distribution Transform normally distributed return into standard deviation score: 𝑟𝑖 − 𝐸(𝑟𝑖 ) 𝑠𝑟𝑖 = 𝜎𝑖 Original return, given standard normal return: 𝑟𝑖 = 𝐸 𝑟𝑖 + 𝑠𝑟𝑖 × 𝜎𝑖 Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 14  Figure 5.3 Normal Distribution r = 10% and σ = 20% Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 15  5.3 Risk and Risk Premiums Normality over Time When returns over very short time periods are normally distributed, HPRs up to 1 month can be treated as normal Use continuously compounded rates where normality plays crucial role Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 16  5.3 Risk and Risk Premiums: Value at Risk Value at risk (VaR): Measure of downside risk Worst loss with given probability, usually 1% or 5% Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 17  5.3 Risk and Risk Premiums Deviation from Normality and Value at Risk Kurtosis: Measure of fatness of tails of probability distribution; indicates likelihood of extreme outcomes Skew: Measure of asymmetry of probability distribution The Sharpe (Reward-to-Volatility) Ratio Ratio of portfolio risk premium to standard deviation Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 18  5.3 Risk and Risk Premiums Risk Premiums and Risk Aversion Risk-free rate: Rate of return that can be earned with certainty Risk premium: Expected return in excess of that on risk-free securities Excess return: Rate of return in excess of risk- free rate Risk aversion: Reluctance to accept risk Price of risk: Ratio of risk premium to variance Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 19  5.3 Risk and Risk Premiums Mean-Variance Analysis Ranking portfolios by Sharpe ratios Portfolio Risk Premium E (rp ) − rf SP = Standard Deviation of Excess Returns P where E (rp ) = Expected Return of the portfolio rf = Risk Free rate of return  P = Standard Deviation of portfolio excess return Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 20  5.4 The Historical Record Using Time Series of Return Scenario analysis derived from sample history of returns Variance and standard deviation estimates from time series of returns: 1 Var (rt ) =   ( rt − rt ) 2 n −1 SD (rt ) = Var (rt ) 1 rt =  rt n Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 21  5.4 The Historical Record: World Portfolios World Large stocks: 24 developed countries, ~6000 stocks U.S. large stocks: Standard & Poor's 500 largest cap U.S. small stocks: Smallest 20% on NYSE, NASDAQ, and Amex World bonds: Same countries as World Large stocks U.S. Treasury bonds: Barclay's Long-Term Treasury Bond Index Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 22  Table 5.3: Historical Return and Risk Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 23  Figure 5.4: Treasury Bills Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 24  Figure 5.4: 30-year Treasury Bonds Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 25  Figure 5.4: Common Stocks Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 26  5.5 Asset Allocation across Portfolios Asset Allocation Portfolio choice among broad investment classes Complete Portfolio Entire portfolio, including risky and risk-free assets Capital Allocation Choice between risky and risk-free assets Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 27  5.5 Asset Allocation across Portfolios The Risk-Free Asset Treasury bonds (still affected by inflation) Price-indexed government bonds Money market instruments effectively risk-free Risk of CDs and commercial paper is miniscule compared to most assets Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 28  5.5 Portfolio Asset Allocation: Expected Return and Risk Expected Return of the Complete Portfolio E (rC ) = y  E (rp ) + (1 − y)  r f where E (rC ) = Expected Return of the complete portfolio E (rp ) = Expected Return of the risky portfolio rf = Return of the risk free asset y = Percentage assets in the risky portfolio Standard Deviation of the Complete Portfolio  C = y  p where  C = Standard deviation of the complete portfolio  P = Standard deviation of the risky portfolio Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 29 Figure 5.7 Investment Opportunity Set Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 30  5.5 Asset Allocation across Portfolios Capital Allocation Line (CAL) Plot of risk-return combinations available by varying allocation between risky and risk-free Risk Aversion and Capital Allocation y: Preferred capital allocation Available risk premium to variance ratio y= Required risk premium to variance ratio [ E (rP ) − rf ] /  P2 [ E (rP ) − rf ] = = A A P2 Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 31  5.6 Passive Strategies and the Capital Market Line Passive Strategy Investment policy that avoids security analysis Capital Market Line (CML) Capital allocation line using market-index portfolio as risky asset Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 32 Table 5.5: Excess Returns Statistics for the Market Index Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 33 5.6 Passive Strategies and the Capital Market Line Cost and Benefits of Passive Investing Passive investing is inexpensive and simple Expense ratio of active mutual fund averages 1% Expense ratio of hedge fund averages 1%-2%, plus 10% of returns above risk-free rate Active management offers potential for higher returns Copyright © 2022 McGraw-Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill. 34